HW1

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School

University of Louisville *

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Course

680

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Statistics

Date

Feb 20, 2024

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docx

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Uploaded by CoachCaterpillarMaster1073

Homework Assignment 1: Descriptive Statistics require (mosaic) require (lattice) Hypertension # Systolic Blood Pressure Data in the recumbent position rSystolic = c ( 99 , 126 , 108 , 122 , 104 , 108 , 116 , 106 , 118 , 92 , 110 , 138 , 120 , 142 , 118 , 134 , 118 , 126 , 108 , 136 , 110 , 120 , 108 , 132 , 102 , 118 , 116 , 118 , 110 , 122 , 106 , 146 ) # Diastolic Blood Pressure Data in the recumbent position rDiastolic = c ( 71 , 74 , 72 , 68 , 64 , 60 , 70 , 74 , 82 , 58 , 78 , 80 , 70 , 88 , 58 , 76 , 72 , 78 , 78 , 86 , 78 , 74 , 74 , 92 , 68 , 70 , 76 , 80 , 74 , 72 , 62 , 90 ) # Systolic Blood Pressure Data in the standing position sSystolic = c ( 105 , 124 , 102 , 114 , 96 , 96 , 106 , 106 , 120 , 88 , 102 , 124 , 118 , 136 , 92 , 126 , 108 , 114 , 94 , 144 , 100 , 106 , 94 , 128 , 96 , 102 , 88 , 100 , 96 , 118 , 94 , 138 ) # Diastolic Blood Pressure Data in the standing position sDiastolic = c ( 79 , 76 , 68 , 72 , 62 , 56 , 70 , 76 , 90 , 60 , 80 , 76 , 84 , 90 , 58 , 68 , 68 , 76 , 70 , 88 , 64 , 70 , 74 , 88 , 64 , 68 , 60 , 84 , 70 , 78 , 56 , 94 ) # Combining all variables into one data frame bloodPressureData = data.frame (rSystolic, rDiastolic, sSystolic, sDiastolic) # Storing difference in systolic and diastolic blood pressures as variables systolicDiff = bloodPressureData $ rSystolic - bloodPressureData $ sSystolic diastolicDiff = bloodPressureData $ rDiastolic - bloodPressureData $ sDiastolic print (systolicDiff) ## [1] -6 2 6 8 8 12 10 0 -2 4 8 14 2 6 26 8 10 12 14 -8 10 14 14 4 6 ## [26] 16 28 18 14 4 12 8 Problem 2.19 The average blood pressure difference (recumbent - standing) for systolic blood pressure is 8.8125 mm Hg, while for diastolic blood pressure it is 0.9375 mm Hg. The median blood

pressure difference for systolic blood pressure is 8 mm Hg, and for diastolic blood pressure, it is 1 mm Hg. # Store the mean of the differences as variables systolicDiffMean = mean (systolicDiff) diastolicDiffMean = mean (diastolicDiff) #Store the median of the differences as variables systolicDiffMedian = median (systolicDiff) diastolicDiffMedian = median (diastolicDiff) Problem 2.20 The diastolic difference (recumbent - standing) displays a range from a minimum of -14 mm Hg to a maximum of 16 mm Hg. The lower quartile (Q1) is -2 mm Hg, the median is 1 mm Hg, and the upper quartile (Q3) is 4 mm Hg. On the other hand, the systolic difference (recumbent - standing) ranges from a minimum of -8 mm Hg to a maximum of 28 mm Hg. The Q1 is 4 mm Hg, the median is 8 mm Hg, and the Q3 is 14 mm Hg. # Storing box and whisker plots for the diastolic and systolic blood pressure differences diastolicDiffBoxPlot = bwplot (diastolicDiff, main= "Berhe: Diastolic Difference BWPlot" ) systolicDiffBoxPlot = bwplot (systolicDiff, main= "Berhe: Systolic Difference BWPlot" ) Problem 2.21 Examining the variances in systolic blood pressure between the recumbent and standing positions reveals a slight elevation in blood pressure while in the recumbent position. Conversely, analyzing diastolic blood pressure across both positions yields inconsistent findings, suggesting that position exerts minimal influence on diastolic blood pressure overall. print (diastolicDiff) ## [1] -8 -2 4 -4 2 4 0 -2 -8 -2 -2 4 -14 -2 0 8 4 2 8 ## [20] -2 14 4 0 4 4 2 16 -4 4 -6 6 -4 print (systolicDiff) ## [1] -6 2 6 8 8 12 10 0 -2 4 8 14 2 6 26 8 10 12 14 -8 10 14 14 4 6 ## [26] 16 28 18 14 4 12 8

Problem 2.22 An atypical change in systolic blood pressure when transitioning from a recumbent to standing position is defined as any deviation outside the normal range of 0 to 16 units. # Using the quantile function to get the bottom and lower decile of the systolic difference dataset upperSystolicDecile = quantile (systolicDiff, 0.9 , type= 2 ) lowerSystolicDecile = quantile (systolicDiff, 0.1 , type= 2 ) Environmental Health, Pediatrics # Set Working Directory to gain access to lead data file setwd ( "C: \\ Users \\ ggber \\ OneDrive \\ Desktop \\ R Work \\ PHST680 \\ Week 1 Homework \\ " ) # Read the LEAD.DAT file and convert it to a table leadData = read.table ( file= "LEAD.DAT.txt" , header= TRUE , sep = "," ) newVars = c ( "area" , "sex" , "iq_type" , "lead_grp" , "Group" , "fst2yrs" , "pica" , "colic" , "irrit" , "convul" ) leadData[,newVars] = lapply (leadData[,newVars],factor) Problem 2.31 The average age of children in the control group is 9.33 years, whereas those in the exposed group average 8.27 years. Typically, children in the control group are older by approximately one year compared to those in the exposed group. This contrast is visually represented through parallel box plots, with the exposed group's plot positioned above the control group's. These plots offer a clear comparison of the 25th and 75th percentiles as well as the median age for both groups. In both numerical and graphical summaries, the control group consistently displays higher age values than the exposed group. Regarding lead exposure based on gender, a greater proportion of males than females have been exposed to lead. Additionally, regardless of gender, the number of individuals without exposure surpasses those who have been exposed. # Numeric Summary of age by group favstats ( ~ ageyrs | Group, data= leadData) ## Group min Q1 median Q3 max mean sd n missing ## 1 1 3.75 6.5000 9.420 12.560 15.92 9.327308 3.572386 78 0 ## 2 2 3.75 5.2725 7.835 10.335 15.25 8.269783 3.411756 46 0 # Graphic Summary of age by group bwplot (Group ~ ageyrs, data= leadData)

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#Numeric Summary of Gender by Group male = subset (leadData, sex == 1 ) female = subset (leadData, sex == 2 ) # Graphical Display of Gender by Group maleGraph = bargraph ( ~ Group, data= male, main= "Male" ) femaleGraph = bargraph ( ~ Group, data= female, main= "Female" ) print (maleGraph)

print (femaleGraph)

Problem 2.32 Regarding verbal IQ, the exposed group demonstrates less variability and more consistent performance in their verbal IQ scores compared to the non-exposed group. Although they exhibit a higher lower quartile (Q1), their upper quartile (Q3) is lower than that of the non- exposed group. The median scores for both groups are very similar, with the exposed group at 29.5 and the non-exposed group at 30. Additionally, the non-exposed group has a higher standard deviation of 9.26 compared to the exposed group's 7.34. In summary, individuals not exposed to lead generally achieve significantly higher verbal IQ scores compared to those exposed to lead. Regarding performance IQ, the exposed group also shows less variability in scores compared to the non-exposed group. Although their Q1 is higher, their Q3 is lower than that of the non-exposed group. The median score for the exposed group is lower at 38, while the non-exposed group has a median of 41. Furthermore, the non-exposed group has a higher standard deviation of 9.69 compared to the exposed group's 7.74. In summary, individuals not exposed to lead generally achieve higher performance IQ scores compared to those exposed to lead. # Numeric Summary of verbal IQ by group favstats ( ~ iqv_raw | Group, data= leadData) ## Group min Q1 median Q3 max mean sd n missing ## 1 1 13 23 30.0 37 57 30.57692 9.258929 78 0 ## 2 2 9 25 29.5 34 50 29.65217 7.340050 46 0 # Graphic Summary of verbal IQ by group bwplot (Group ~ iqv_raw, data= leadData)

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# Numeric Summary of performance IQ by group favstats ( ~ iqp_raw | Group, data= leadData) ## Group min Q1 median Q3 max mean sd n missing ## 1 1 12 35.00 41 47.00 68 41.39744 9.685093 78 0 ## 2 2 12 31.25 38 42.75 52 36.97826 7.744501 46 0 # Graphic Summary of performance IQ by group bwplot (Group ~ iqp_raw, data= leadData)

HW1

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